Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
Unsigned basic expectation
Basic expectation
Random real number moment
Random real number central moment
Absolute central moment
Random real number variance
Index of dispersion
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \mathbb{E} |X|^2 < \infty \end{equation}
(ii) \begin{equation} \mathbb{E} X \neq 0 \end{equation}
The index of dispersion of $X$ is the D993: Real number \begin{equation} \text{Disp} X : = \frac{\text{Var} X}{\mathbb{E} X} \end{equation}
Also known as
Variance-to-mean ratio, Variance-to-expectation ratio, Dispersion-to-location ratio
Child definitions
» D5276: Equidispersed random basic real number
» D5277: Index of variation
» D5274: Overdispersed random basic real number
» D5275: Underdispered random basic real number